Joseph placed either the interpreters or the seer stone in a hat, pressed his face into the hat to block out extraneous light, and read aloud the English words that appeared on the instrument.—The Church of Jesus Christ of Latter-day Saints, Gospel Topics (2013) off-site

Question: How exactly did Joseph Smith translate the gold plates?

Joseph Smith only stated that he translated the Book of Mormon by the "gift and power of God"

All that we know for certain is that Joseph translated the record "by the gift and power of God." (D&C 135:3) We are given some insight into the spiritual aspect of the translation process, when the Lord says to Oliver Cowdery:

"But, behold, I say unto you, that you must study it out in your mind; then you must ask me if it be right, and if it is right I will cause that your bosom shall burn within you; therefore, you shall feel that it is right." (D&C 9:8)

Beyond this, the Church does not take any sort of official stand on the exact method by which the Book of Mormon translation occurred. Joseph Smith himself never recorded the precise physical details of the method of translation:

"Brother Joseph Smith, Jun., said that it was not intended to tell the world all the particulars of the coming forth of the Book of Mormon; and also said that it was not expedient for him to relate these things"[1]

It is important to remember that what we do know for certain is that the translation of the Book of Mormon was carried out "by the gift and power of God." These are the only words that Joseph Smith himself used to describe the translation process.

Gospel Topics: "According to these accounts, Joseph placed either the interpreters or the seer stone in a hat, pressed his face into the hat to block out extraneous light, and read aloud the English words"

Gospel Topics on LDS.org:

[T]he scribes and others who observed the translation left numerous accounts that give insight into the process. Some accounts indicate that Joseph studied the characters on the plates. Most of the accounts speak of Joseph’s use of the Urim and Thummim (either the interpreters or the seer stone), and many accounts refer to his use of a single stone. According to these accounts, Joseph placed either the interpreters or the seer stone in a hat, pressed his face into the hat to block out extraneous light, and read aloud the English words that appeared on the instrument. The process as described brings to mind a passage from the Book of Mormon that speaks of God preparing “a stone, which shall shine forth in darkness unto light.”[2]

Russell M. Nelson: "The details of this miraculous method of translation are still not fully known. Yet we do have a few precious insights"

Russell M. Nelson:

The details of this miraculous method of translation are still not fully known. Yet we do have a few precious insights. David Whitmer wrote: “Joseph Smith would put the seer stone into a hat, and put his face in the hat, drawing it closely around his face to exclude the light; and in the darkness the spiritual light would shine. A piece of something resembling parchment would appear, and on that appeared the writing. One character at a time would appear, and under it was the interpretation in English. Brother Joseph would read off the English to Oliver Cowdery, who was his principal scribe, and when it was written down and repeated to Brother Joseph to see if it was correct, then it would disappear, and another character with the interpretation would appear. Thus the Book of Mormon was translated by the gift and power of God, and not by any power of man.” (David Whitmer, An Address to All Believers in Christ, Richmond, Mo.: n.p., 1887, p. 12.)[3]

Marcus B. Nash: "This was dictated, word by word, as he looked into instruments the Lord prepared for him, using a hat to shield his eyes from extraneous light"

Marcus B. Nash:

This was not a composition. This was dictated, word by word, as he looked into instruments the Lord prepared for him, using a hat to shield his eyes from extraneous light in order to plainly see the words as they appeared. Contrary to one who translates with the use of a dictionary, as it were, the translation was revelation flowing to him from heaven, and written by scribes (with the inevitable scrivener errors). [4]—(Click here to continue)

Nicholson: "This essay focuses primarily on the methods and instruments used in the translation process and how a faithful Latter-day Saint might view these as further evidence of truthfulness of the restored Gospel"

Roger Nicholson:

This essay seeks to examine the Book of Mormon translation method from the perspective of a regular, nonscholarly, believing member in the twenty-first century, by taking into account both what is learned in Church and what can be learned from historical records that are now easily available. What do we know? What should we know? How can a believing Latter-day Saint reconcile apparently conflicting accounts of the translation process? An examination of the historical sources is used to provide us with a fuller and more complete understanding of the complexity that exists in the early events of the Restoration. These accounts come from both believing and nonbelieving sources, and some skepticism ought to be employed in choosing to accept some of the interpretations offered by some of these sources as fact. However, an examination of these sources provides a larger picture, and the answers to these questions provide an enlightening look into Church history and the evolution of the translation story. This essay focuses primarily on the methods and instruments used in the translation process and how a faithful Latter-day Saint might view these as further evidence of truthfulness of the restored Gospel.[5]—(Click here to continue)

Gardner: "What we will be looking at is the idea that this whole concept of the seer stone working...it’s stone that becomes the trigger that allows the seer to do what the seer does"

Brant Gardner:

A seer stone is a rock. We have seer stones. The church still has them, I’ve seen them. At one point in time I remember going on the temple square and going through the museum there and I saw one and I looked at it and I saw a rock. I didn’t see the translation, I didn’t see anything else I saw a rock. I can pretty much guarantee you that the vast majority of us as we would look at that rock would see, a rock. That does not mean that something isn’t working because they were looking at the rock and that’s what we have to look at. What we will be looking at is the idea that this whole concept of the seer stone working “It’s the seer that’s working,” and it’s stone that becomes the trigger that allows the seer to do what the seer does. So that’s kind of step one and we will talk about how that happens.[6]—(Click here to continue)

↑Roger Nicholson, "The Spectacles, the Stone, the Hat, and the Book: A Twenty-first Century Believer’s View of the Book of Mormon Translation," Interpreter: A Journal of Mormon Scripture 5:121-190 (7 June 2013).